In the given figure PQ - RS- TR - QU and - PTR - 42- Find - QUR-

Since, PQ nbsp; and RS are parallel and TR is transversal, nbsp; Therefore, nbsp; nbsp;∠ PTR= ∠ TRU [alternate interior angles] ...

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Standard VI

Mathematics

Types of Angles

In the given ...

Question

In the given figure PQ || RS, TR || QU and $∠ P T R = 42^{\circ}$ . Find $∠ Q U R .$

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Solution

Since, PQ and RS are parallel and TR is transversal,
Therefore,
$∠ P T R = ∠ T R U [a l t e r n a t e i n t e r i o r a n g l e s] \Rightarrow ∠ T R U = 42^{\circ}$
Now, TR is parallel to QU and RS is transversal.
Therefore, $∠ T R U + ∠ R U Q = 180^{\circ} [c o n s e c u t i v e i n t e r i o r a n g l e s] \Rightarrow 42^{\circ} + ∠ R U Q = 180^{\circ} \Rightarrow ∠ R U Q = 180^{\circ} - 42^{\circ} = 138^{\circ}$

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In the given figure PQ || RS, TR || QU and ∠PTR=42∘. Find ∠QUR.

Since, PQ and RS are parallel and TR is transversal, Therefore, ∠PTR=∠TRU [alternate interior angles]⇒∠TRU=42∘ Now, TR is parallel to QU and RS is transversal. Therefore, ∠TRU+∠RUQ=180∘ [consecutive interior angles]⇒42∘+∠RUQ=180∘⇒∠RUQ=180∘−42∘=138∘

In the given figure PQ || RS, TR || QU and $∠ P T R = 42^{\circ}$ . Find $∠ Q U R .$